Approximating solutions of equations using Newton's method with a modified Newton's method iterate as a starting point
Keywords:Banach space, Newton-Kantorovich method, radius of convergence, Fréchet-derivative, Banach lemma on invertible operators
AbstractIn this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before -. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations in a Banach space setting. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before -. Numerical examples are also provided.
How to Cite
Argyros, I. (2007). Approximating solutions of equations using Newton’s method with a modified Newton’s method iterate as a starting point. Rev. Anal. Numér. ThéOr. Approx., 36(2), 123-137. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art2